(j+6)(j-1)=0

Solution for (j+6)(j-1)=0 equation:

Simplifying
(j + 6)(j + -1) = 0

Reorder the terms:
(6 + j)(j + -1) = 0

Reorder the terms:
(6 + j)(-1 + j) = 0

Multiply (6 + j) * (-1 + j)
(6(-1 + j) + j(-1 + j)) = 0
((-1 * 6 + j * 6) + j(-1 + j)) = 0
((-6 + 6j) + j(-1 + j)) = 0
(-6 + 6j + (-1 * j + j * j)) = 0
(-6 + 6j + (-1j + j2)) = 0

Combine like terms: 6j + -1j = 5j
(-6 + 5j + j2) = 0

Solving
-6 + 5j + j2 = 0

Solving for variable 'j'.

Factor a trinomial.
(-6 + -1j)(1 + -1j) = 0

Subproblem 1
Set the factor '(-6 + -1j)' equal to zero and attempt to solve:

Simplifying
-6 + -1j = 0

Solving
-6 + -1j = 0

Move all terms containing j to the left, all other terms to the right.

Add '6' to each side of the equation.
-6 + 6 + -1j = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1j = 0 + 6
-1j = 0 + 6

Combine like terms: 0 + 6 = 6
-1j = 6

Divide each side by '-1'.
j = -6

Simplifying
j = -6
Subproblem 2
Set the factor '(1 + -1j)' equal to zero and attempt to solve:

Simplifying
1 + -1j = 0

Solving
1 + -1j = 0

Move all terms containing j to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1j = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1j = 0 + -1
-1j = 0 + -1

Combine like terms: 0 + -1 = -1
-1j = -1

Divide each side by '-1'.
j = 1

Simplifying
j = 1
Solution
j = {-6, 1}